Re: A Record Prime Factor by Pollard's "p-1" method

On Sun, 04 March 2001, Andy Steward wrote: [On the NMBRTHRY mailing list] ... Well done, Andy. Is UBasic as fast for this kind of job as C would be with one of

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, Mar 5 1:45 AM

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On Sun, 04 March 2001, Andy Steward wrote:
[On the NMBRTHRY mailing list]
> Early on 3rd March 2001, my own Ubasic "p-1" code found the following
> factor of 922^47-1:
>
> p39=188879386195169498836498369376071664143
> p-1=2.3.13.47.101.813613.1174951.1766201.3026227.99836987
>
> I therefore claim the world record factor found by this method (unless
> any of you know better).

Well done, Andy.
Is UBasic as fast for this kind of job as C would be with one of the standard bignum packages. Or a dedicated number-theoretic package, such as pari or LiDIA?

I was looking on the prime pages, for some info on the p-1 factoring method, and I noticed that there is no "Factoring into primes" section on the prime pages. My favourite search engine quickly pointed me in the direction of Wolfram/Eric Weisstein's Mathworld, several dead links, and some source code in an unknown language... So perhaps we could put our heads together to create the kernel of a new prime pages page of factoring methods? As far as my memory serves me (traditionally very poorly), it would be nice to get information on the following.
- Trial division
- Pollard p-1
- Pollard p+1
- Continued Fractions
- Pollard Rho
- NFS
- ECM
Note - I haven't got a clue what any of the above are (apart from one), I'm just parroting.

I do have Knuth, so I am prepared to put my reading spec's on to learn a few of the above, but that still leaves half of them for others.